Question: Let $f(x) = 7x^{2}+10x+2$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Answer: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}+10x+2 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = 10, c = 2$ $ x = \dfrac{-10 \pm \sqrt{10^{2} - 4 \cdot 7 \cdot 2}}{2 \cdot 7}$ $ x = \dfrac{-10 \pm \sqrt{44}}{14}$ $ x = \dfrac{-10 \pm 2\sqrt{11}}{14}$ $x =\dfrac{-5 \pm \sqrt{11}}{7}$